Maharashtra BoardEnglish MediumSTD 8MathsCubes and Cube Roots2 Marks
Question
Which of the following number are not perfect cube?
216
✓
Answer
On factorising 216 into prime factors, we get:
216 = 2 × 2 × 2 × 3 × 3 × 3
On grouping the factors in triples of equal factors, we get:
216 = {2 × 2 × 2} × {3 × 3 × 3}
It is evident that the prime factors of 216 can be grouped into triples of equal factors and no factor is left over. Therefore, 216 is a perfect cube.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.